This video explains how to choose an effective domain name for your site – balancing up the needs for personal/company branding with Search Engine Optimisation considerations.
It shows the relationship between domain names and website hosting, and goes through the practical steps needed to register a domain.
You may need to right-click the following links and select Save Target As/Save Link As to download the file to your computer
Recommended Resources for Domain Registration
Usually best and cheapest to use a registrar in the country of the site you want to register.
For US sites I use GoDaddy.
For UK sites I use 123-reg.
Though in all honesty any decent registrar will do.
A useful tool when looking for available domains is Domize which checks availability and can also do “wildcard” searches for domains.: